well-tempered

To be tuned in accordance with a synthentic system of Western tonality based on the semi-tone making all 24 keys equally viable.

The subject of tonality, temperment and tuning is complex. It encompasses acoustics, mathematics, music theory, technology, psychology and cultural history. There are a variety of resources that well document territory. What follows is a very brief, practical summary to provide some insight into the meaning of Bach's title, the Well-Tempered Clavier.

The musical scales commonly used in Western music have a basis in natural, physical phenomena. It is possible to abstract a mathematical model from nature to determine a precise set of frequencies for all the discrete tones in a particular key and to use those values as an absolute reference for musicians and instruments. The result is "pure" or "perfect", rooted as it is, in nature.

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